Seydou Doumbia converted the follow up after David de Gea had tipped Roman Eremenko's spot-kick on to the post, but Martial ensured the match ended in a 1-1 draw with a second-half header.
In the first half United performed poorly on the return to the city where they lifted the Champions League in 2008.
De Gea saved brilliantly to deny Ahmed Musa in the Khimki Arena after Doumbia had put the hosts ahead.
But Louis van Gaal's men improved after the break and they just about deserved to take home the point that ensures they remain second in Group B.
The CSKA fans did their best to raise the temperature inside the ground before kick-off.
They held a huge surfer flag aloft, hailing CSKA coach Leonid Slutsky as 'The Exorcist' in charge of expelling the Red Devils from their stadium.
CSKA put maximum pressure on United from the off, pressing high up the pitch to deny the visitors any space.
Jesse Lingard, making his Champions League debut, showed signs of promise but could not prise open a rigid CSKA defence.
At the other end of the pitch former United midfielder Zoran Tosic fired an early shot wide and Mario Fernandes caused Matteo Darmian problems with his pace down the flank.
And with 15 minutes gone, the right-back won a penalty for CSKA.
Fernandes lifted the ball over Martial and drew a fine save from De Gea. United thought the danger had passed but referee Carlos Velasco Carballo spotted the France striker had handled the ball and pointed to the spot.
De Gea tipped Eremenko's penalty on to the post but the ball bounced into Doumbia's path off the goalkeeper's legs and he tucked the ball away.
United would have been 2-0 down soon after had De Gea not tipped over Musa's chip.
Rooney drew the first save of the match from Igor Akinfeev in the 32nd minute but the CSKA goalkeeper had nothing else to do before the half-time whistle.
Van Gaal brought Marouane Fellaini on for Bastian Schweinsteiger at the break. Little changed initially but United then started to improve.
Rooney then glanced the ball into Akinfeev's arms from Ander Herrera's cross.
The away fans held their breath as Musa entered the box after a CSKA break but he drilled into De Gea's arms and United went on the attack again.
Finally the pressure paid off. Herrera sent Antonio Valencia down the right flank and he whipped in a low ball for Martial, who beat Akinfeev with a diving header.
United pushed for a winner as CSKA tired. Rooney appealed for a penalty in the dying minutes when the ball appeared to touch the arm of a red shirt.
Memphis Depay came on for Lingard, but did not make a telling impact and United had to make do with a point from their trek east.
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